The radius r of the smallest circular paper plate that holds a pizza of a given
ID: 3889116 • Letter: T
Question
The radius r of the smallest circular paper plate that holds a pizza of a given radius R=5 inches and central angle q, 0 < q £ p, is given by the function r=f(q) where:
1. Sketch the pizza in its plate for q = p/6 (a 30 degree wedge). Find r for q = p/6.
2. Sketch the pizza in its plate for q = p (half the pizza). Find r for q = p.
3. Determine the function f(q) for the domain p £ q £ 2p.
4. Explain how to obtain the formula above for the function f(q) on (0,p). Hint: Sketch lots of examples.
5. Use MATLAB to create and print a graph of f(q). (printed graph to be submitted separately to professor.)
if you can, you can draw the graph on paper.
A wedge of pizza. (Yum!)Explanation / Answer
A circle with
center
A and
radius
r
is the set
of all points a distance
r
from the point A. For instance, if you pick the center of your screen as A
and 3
cm
s
r
, then all of the points on the screen that are 3
cm a
way from the center
form a circle.
An easy way to draw a circle is to hold a string fixed at one end (for instance, with a pin) and
attach a pen to the other end. Holding the string taut and drawing wherever the taut string allows
gives a circle. This is the same technique yo
u follow when using a compass. With a compass, the
string is simply replaced by a metal or plastic structure, which usually has some markings to let
you pick the radius of your circle.